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Mathematical Communications, Vol. 17 No. 1, 2012.

Original scientific paper

General rotational surfaces in Euclidean space $\mathbb{E}^4$ with pointwise 1-type Gauss map

Uğur Dursun ; Department of Mathematics, Faculty of Science andLetters, Istanbul Technical University, Maslak, Istanbul, Turkey
Nurretin Cenk Turgay ; Department of Mathematics, Faculty of Science andLetters, Istanbul Technical University, Maslak, Istanbul, Turkey

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Abstract

In this paper, we study general rotational surfaces in $\mathbb E^4$ with pointwise 1-type Gauss map.
We consider general rotational surfaces in $\mathbb E^4$ whose meridian curves lie in two-dimensional planes.
We firstly obtain all general rotational surfaces in $\mathbb E^4$
with proper pointwise 1-type Gauss map of the first kind.
Then we classify minimal rotational surfaces of $\mathbb E^4$
with proper pointwise 1-type Gauss map of the second kind.

Keywords

Rotational surfaces; minimal surface; normal bundle; mean curvature; pointwise 1-type; Gauss map

Hrčak ID:

82985

URI

https://hrcak.srce.hr/82985

Publication date:

12.6.2012.

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